numerical study of a buckling restrained brace (brb) in
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Makara J. Technol. 25/1 (2021), 3747
doi: 10.7454/mst.v25i1.3908
April 2021 | Vol. 25 | No. 1 37
Numerical Study of a Buckling Restrained Brace (BRB) in Steel Structures and
Comparison with a Convergent Ordinary Brace (OCB) Under Static and
Dynamic Loading
Fatemeh Habibpour*
Lecturer, Faculty of Civil Engineering, Ayandegan Institute of Higher Education, Tonekabon, Iran
*E-mail: fatemehhabibpour0098@gmail.com
Abstract
Bulk metallic glass (BMG) has good mechanical strength, high hardness, wear resistance, and corrosion resistance with
promising application in various industries. However, for the industrial production of BMG, the main issue is how to
overcome limitations of joining with other materials. The present study focuses on solder processing at low operating
temperature to avoid exceeding the recrystallization temperature. A feasible joining process for BMG was developed using
lead-free solders. The BMG surface is pre-plated with copper, nickel, or titanium as a wetting layer. The reaction
temperature is set between the glass transition temperature of BMG and the melting point of the solder. After a reflowing
and aging process, the joint sample was examined using SEM, EDS, EPMA, and XRD. The Cu–Zr based BMG can be
successfully joined with Sn-58Bi solder after plating Cu on the BMG surface. A diffusion layer was observed and the
thickness increased with longer aging time. The main components of the diffusion layer are ZrO2 and Cu10Zr7.
Abstrak
Kajian Numerik Penjepit yang Ditahan Menekuk (BRB) pada Struktur-struktur Baja dan Perbandingan dengan
Penjepit Biasa yang Konvergen (OCB) dengan Pembebanan Statis dan Dinamis. Filosofi rancangan gedung-gedung
tahan gempa bumi telah mengalami banyak perubahan dalam tahun-tahun belakangan ini. Banyak sruktur yang dirancang
dengan metode-metode tradisional, dan juga pengembangan metode-metode analisis serta kemajuan kinerja kompuer yang
signifikan, merupakan faktor-faktor yang memberi kontribusi pada perubahan-perubahan tersebut. Di dalam kajian ini,
ketahanan sruktur baja yang dijepit diinvestigasi dengan menggunakan penjepit yang ditahan menekuk (buckling
restrained braces (BRB)) dan dibandingkan dengan suatu penjepit biasa yang konvergen (a convergent ordinary brace
(OCB)). Gedung-gedung dengan 5, 8, 10, dan 12 lantai yang rancangannya buruk diperkokoh dengan BRB dan kinerjanya
diinvestigasi dengan menggunakan analisis statis dan dinamis non linier. Di dalam kajian ini, penguatan bagian-bagian
struktur lainnya pada penjepit tersebut diinvestigasi. Hasil-hasilnya menunjukkan bahwa pengurangan sambungan plastis
pada perpindahan ruang antara BRB k arah rangka-rangka pada pnjepit konvnsional lbih kcil karena menurunnya prilaku
plastis sambungan dan distribusi prpindahan rlatif pada ruang antara.
Keywords: BRB brace, improvement, non-linear static analyses, non-linear dynamic analysis, reinforcement of steel
structure
1. Introduction
Reducing the vulnerability of buildings against earthquakes
has presented a major challenge to designers and
practitioners. The importance of this issue is increasing
because of building wear in earthquake zones,
construction of buildings without standards and instead
using the old design regulations, which has doubled in
the past few decades. Therefore, seismic rehabilitation
of existing buildings in terms of building construction
engineering programs has been proposed. According to
earthquake engineering science and advances in seismic
design regulations, the question arises to whether the
structures that have been designed based on the old
regulations could meet the new provisions; otherwise
the building must be strengthened to comply with the
new regulations [1]. These changes may increase based
on building importance, the addition of a stipulation to
the conditions of the regularity (well-organization) of
the building in the plan, changing the formulas of the
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38
building response factor (B), and the building behavior
factor (R) for some structural systems, which changes
the seismic lateral response forces. Therefore, the
structures modeled according to the old regulations do
not respond under the same conditions based on seismic
provisions of steel structures, and they need to be
strengthened [2].
A weakness of common frames is the difference between
tensile and compressive strengths; consequently, the
resistance declines under encountering cyclic loading.
In a buckling restrained brace (BRB), the nucleus
should be designed in a way that both compression and
tension is acceptable. To prevent ultimate buckling in
compression, the nucleus is placed within a steel tube
and the space between the tube and steel nucleus is
filled with mortar or concrete. Before pouring the
mortar, a non-sticky mortar is placed in the empty space
between the nucleus and mortar [3].
The main issue with conventional braced systems with a
special concentric brace is the difference of tensional
and compressive capacity such that in severe
earthquakes when the compressive brace is buckled,
tensional brace tolerates high non-elastic cycle
deformations. As a result, in multi-story buildings
braced with special concentric bracelets with decreasing
hardness and resistances by buckling, the concentrated
non-elastic lateral deformations in that story will
increase [4–7].
Faghihmaleki et al. [8] compared the behavior of special
concentric braced frames with buckling bracelets. Non-
linear static analysis with periodical loading was
performed on the frames. The results indicate a more
formative and stable behavior of the buckling bracelet
than a conventional bracelet. Additionally, the effect of
the primary geometric defect is significant only in the
initial displacement steps and of the percentage of strain
hardening is greater, the structure shows greater
sustainability against higher forces.
Ariyaratana and Fahnestock [9] investigated the reserve
strength generated by members of the rigid brace in a
lateral load-resistant system to improve the seismic
performance of the buckling brace. These two modes
with storage resistance can be used together or
separately, which leads to system diversity.
Asgarian and Shokrgozar [10] presented the response
modification factor of structures with buckling brace
frames and in this study, the traction capability and
response modification factor of buckling brace frames
were investigated. using linear and non-linear static
analysis, linear dynamics, non-linear dynamics on
building models with different brace using OpenSees
software. They surveyed the effect of parameters on
response modification factors, such as the height of the
building and the type of system brace. In this article, the
behavior factor was determined for the brace systems.
In conclusion, the behavior factor decreased by
increasing the number of stories.
Chang et al. [11] performed a set of 3D non-linear time
history analysis for six building samples. They used
ordinary earthquakes and nearby areas, and three limit
modes were considered. Using the definition of limit
modes and relative displacement limit of the proposed
story by FEMA356, they calculated the probability of
the fracture. The pressure showed that the effect of the
braced frames can be considerably changed with the
ground and height movement of the building. Added
bracing frames helps to reduce the story drift and
decreases the fracture probability against conventional
movements of the ground. This effect is especially
obvious for a building with a low height. In comparison,
the bending frame system has lower lateral
displacement toward two modes of bracing for near
ground movements.
Manfredi and Sarno [12] evaluated the performance of
reinforced concrete structures and also investigated the
seismic performance of reinforced concrete frames for
gravity loads, which showed little lateral strength in
their model. To solve this problem, they examined BRB
frames and OCB frames using non-linear and dynamic
static analyses and found that the lateral displacement
was reduced in the model with BRBs.
In 2021, Akcelyan et al. [13] proposed a rate-dependent
model for low-yield stress buckling restrained braces
and a procedure for calibrating the input parameters of
the new simulation model. They illustrated two different
ways for non-linear frame analysis with the proposed
model and validated the proposed model with
component BRB experiments.
In 2020, Dong el al. [14] investigated full-scale glulam
frames with BRBs under cyclic loading. They proposed
two types of timber–steel interface connections, strong
and stiff, to work with BRBs efficiently and proved the
capacity design approach. The BRBs improved the glulam
frames’ strength, stiffness, and energy dissipation.
In 2021, Castaldo et al. [15] retrofitted an existing 3D
RC structure using BRBs. They assessed the influence
of the masonry infills on the seismic performance of the
structure and evaluated the performance of the. Finally,
demand hazard curves for the different EDPs and
structural models were performed.
In this study, a braced steel structure resistance using
BRB was compared with OCB. To do this, buildings
with 5, 8, 10, and 12 floors that were poorly designed
were reinforced with BRB and their performance was
investigated using non-linear dynamic and static analyses.
Study of a Buckling Restrained Brace (BRB) in Steel Structures
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2. Introducing the Structures
To survey the strengthening of the steel moment frame
structures against earthquakes using BRB, 8 frames,
including 4 frames with conventional dog bone-shaped
braces and 4 frames with buckling dogbane-shaped
braces with conventional similar sections were selected
in 5, 8, 10, and 12 story buildings. The height of a story
was 3.2 m and the distance between the columns in each
frame was 4 m. Beam connection is simple and the
column connection is the hinge. The chief system was
loin and at last, all points move a story together.
Therefore, there is no force and axial deformation.
SAP2000 software Ver. 18 was used for modeling. The
plan of the buildings is considered in the same form
(Figure 1). Two lateral openings of peripheral frames
have dog bone-shaped braces (Figure s2 and 3). Table 1
shows the sections used in the modeling. In addition, the
building was considered completely regular in the plan
and the usage of the building frames was residential.
The beams and columns were ST37 steel with tension of
Fy=2400 MPa. The maximum of allowed tension is
1/1𝐹𝑦 = 2640. The loading of frames was based on
ASCE7-16 regulation, Edition 2016 [16]. The structures
are assumed to have been built in Tehran. This structure
was built with average importance in an area with very
high relative danger and on ш type soil [17]. In this
research, the size of the nucleus and tube, and crust
thickness of BRB were 153×19 (mm2) and 3 mm,
respectively. The central nucleus was considered to be
smooth steel ST37 and the surrounding steel crust was
high-strength steel ST52. Additionally, the concrete is
the same usual concrete with compression strength of 21
MPa. There was 2.5 mm of empty space between the
central nucleus and concrete/mortar in each side [18].
The mentioned distance is the same thickness of the
separating layer so that the nucleus, under the effect of
imposed force, enters higher modes, and, consequently,
the buckling brace shows better behavior in cyclic
loadings. The middle concrete and steel crust were in
continuous contact [19],[20].
The frames studied in this research was designed by the
allowed tension method based on the tenth subject of
Iran building national regulation and seismic loading
was based on the analytical static method because of
AISC341-16 regulation, Edition 2016 [20]. By
allocating plastic joints to the beams and columns of the
brace, it was under non-linear static analysis and the
level of their function was calculated based on the
principles of factor method. While the frame cannot
respond to the considerable function level, the frame
allocating weaker sections was under linear static
analysis and then non-linear static, which continued
until displacement of the structure reaches the
displacement of the target.
Figure 1. Plan of the Considered Frames
Figure 3. Eight and Five Story Buildings with Brace
(Frame 1)
Figure 4. Twelve and Ten Story Buildings with Brace
(Frame 1)
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Gravitational loads on the building are dead and alive.
The amount of dead load is based on executive details
of chiefs and walls and the amount of alive loads is
because of the usage of different parts of the building
from ASCE7-16 regulation [16], and it is a linear load
and based on the width of the loading surface of each
frame that is 2 m, which entered on the beams of story.
In this research, seven accelerometers were used to
record the non-linear time history analysis of the
earthquake because the minimum records required for
dynamic analysis of time history was equal to seven
records [17]. Table 2 shows the data for mapping
acceleration. The acceleration of mappings had the
following common features: (a) It is located in one
classification of soil. (b) It is located in a nearly
identical distance from the place of fault. (c) It has
features of the areas far from the fault.
Table 1. The Sections used in the Modeling
Story Column Beam OCB Brace
1 2IPE 600 2IPE 600 2UNP 400
2 2IPE 600 2IPE 600 UNP 380
3 2IPE 550 2IPE 550 UNP 350
4 2IPE 500 2IPE 500 UNP 350
5 2IPE 450 2IPE 450 UNP 320
6 2IPE 450 2IPE 450 UNP 320
7 2IPE 400 2IPE 400 UNP 300
8 2IPE 360 2IPE 360 UNP 280
9 2IPE 360 2IPE 360 UNP 260
10 2IPE 330 2IPE 330 UNP 260
11 2IPE 300 2IPE 300 UNP 240
12 2IPE 300 2IPE 300 UNP 200
Table 2. Data of Mapping Acceleration
PGA (g) Earthquake
Magnitude Earthquake Name Station Name Year Number
0/0416 5/74 Coyote Lake Halles valley 1979 1
0/0367 6/19 Morgan hill Apeel 1E –Hayward 1984 2
0/3821 6/93 Loma Prieta Saratoga – Aloha Ave 1989 3
0/3354 6/69 Northridge LA – Hollywood Stor FF 1994 4
0/2101 6/61 San Fernando LA – Hollywood Stor FF 1971 5
0/2237 5/61 SIERRA LOS ANGELES 1991 6
0/1179 6/33 Victoria Chihuahua 1980 7
Figure 4. Acceleration of the Northridge Earthquake
Figure 4 shows a sample of mapping acceleration
(Northridge earthquake) that used non-linear dynamic
analysis. Table 2 lists other records.
For non-linear static analysis, all frames were pushed
until displacement of the target. In this section, the
factor method was applied for the displacement of the
target. In this method, non-linear static analysis was
conducted first and the base shear curve against the
pushover curve was obtained. The displacement of the
target can be obtained based on the pushover curve. In
the frames were under steady lateral load pattern, the
first mode was triangular. Alternatively, plastic
deformations in the beams and columns of the bending
frame under lateral loads of earthquakes appeared as
plastic joints at the beginning and the end of the beams
and columns. Plastic bending joints (M) were allocated
at the end of the two beams. The axial-bending joint
was allocated 0.475 and 0.525 along the beam and 0.05
and 0.95 along the height of the column. The axial
plastic joint was defined for braces and located in the
middle. Tables 2–4 list the function of frames.
Study of a Buckling Restrained Brace (BRB) in Steel Structures
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3. Analysis of the Modeled Structures
Five Story Structure
Non-linear Static Analysis. For the non-linear static
analysis of the five story structure, three lateral load
patterns of triangular, steady, and first mode were used.
For example, a five story frame with joints under the
triangular lateral load pattern are displayed in Table 3.
As shown in Table 3, some joints pass from life safety
(LS) are more limited in the OCB frame than in BRB,
which indicates the weakness of this type of system.
In this section, graphs of the pushover of the structure
under lateral load patterns are displayed in Figures 5–7.
In a general, the number of plastic joints that passed
from the LS limit was greater in the OCB mode and
caused joints especially in the columns to decrease the
OCB capacity of the horizontal area at the end of the
graph and early submission.
The deformed form of the five story frame from
pushover analysis is displayed in Figure 8.
According to Figure 8, joints in the frames with
conventional brace have a greater limit than in joint
column. In the frames with buckling brace the pressure
will enter the columns and plastic joint is created
because the brace is strong. To improve making plastic
joints, the amount of immediate occupation (IO), LS,
and collapse prevision (CP) are used. B indicates the
stage before non-stop usage. C, D, and E are stages to
complete destruction.
Table 3. Joints in a Five Story Frame under Triangular
Lateral Load Pattern
Type Target
Displacement B IO LS CP C D E
OCB 5.578 1 7 0 0 1 5 0
BRB 4.47 0 1 0 0 0 0 0
Figure 5. Base Shear Curve-displacement Under Triangular
Lateral Load
Figure 6. Base Shear Curve-displacement under Steady
Lateral Load
Figure 7. Base Shear Curve-displacement under the
Lateral Load of the First Mode
(a) (b)
Figure 8. (a) Plastic Joints in the Structure with a (a)
Conventional Brace and (b) Buckling Brace
under Triangular Lateral Load
For non-linear dynamic analysis of the models, seven
scaled earthquakes, of Coyote Lake, Morgan Hill,
Northridge, Loma Prieta, Sierra Madre, San Fernando,
and Victoria, were applied to evaluate the plastic joints
of a five story frame.
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Non-Linear Dynamic Analysis of a Five Story
Structure
Scaling Mapping Acceleration. Acceleration of the
selected mappings should be based on the method of
AISC 341-16 regulation, Edition 2016 [14]: a) All
mapping accelerations will be scaled as their maximum
amount, which means their maximum acceleration
equals g gravitation acceleration. b) The response
spectrum of acceleration of each couple of scaled
mapping accelerations is determined by a applying 5%
damping ratio. c) Response spectrums of each couple of
mapping accelerations are combined using a square root
method and a combined spectrum will be made for each
couple. d) The spectrums of the combined response of
mapping acceleration couple are averaged and
compared in the range of alternating times 0.2 T and 1.5
T with a standard spectrum. The scale coefficient is
determined such that is in this range, the number of
means in no mode will not be lower than 1.4, its peer
amount in the standard spectrum. T is the time of the
main alternate of the building. e) The factor of
determined scale (Table 4), should be multiplied by the
acceleration of scaled mappings in clause (a) and will be
used in dynamic analysis.
The deformed form of five story frame from the non-
linear time dynamic analysis is displayed in Figure 9.
The number of joints under different mapping
accelerations is displayed in five story frames in Table
5.
Based on Table 4, in the frames with conventional
braces, more joints pass from the LS limit and there is
the maximum of joints. By surveying Figures 14 to 20,
the frames, the number of made joints in the columns
with BRB braces that did not pass from LS limit, is
greater than the frames with OCB brace because BRB
transfers the force to the columns and creates more
joints in this area. However, in the frames with OCB
brace, the plastic joints are created first in the braces
and then in the columns. The displacement and relative
displacement of the story under non-linear time history
is displayed in Figure 10.
Table 4. Scale Factor
Story 5 8 10 12
SC Factor 0.53 0.565 0.682 0.72
Table 5. The Number of Joints under Different Mapping
Accelerations of the Coyote Lake Earthquake
in Five Story Frame
Type B IO LS CP C D E
OCB 4 17 4 0 0 20 0
BRB 6 6 11 0 0 0 5
(OCB)
(BRB)
Figure 9. Plastic Joint in the Structure under the Coyote
Lake Earthquake with a Conventional Brace
and Buckling Brace
Based on the seven mapping accelerations applied to a
five story structure with buckling braces, the
displacement of stories with OCB and BRB had a
decreasing trend. The relative displacement of the story
in comparison with conventional braces had a special
order and low changes were evident in each lower story.
Study of a Buckling Restrained Brace (BRB) in Steel Structures
Makara J. Technol. 1 April 2021 | Vol. 25 | No. 1
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Figure 10. The Maximum of Displacement and Relative
Displacement of Stories under the Coyote Lake
Earthquake
Story Structure
Plastic Joints in an Eight Story Frame under Lateral
Loads. In this section, also for determining the function
of frames in making the plastic joint, (Table 6).
As shown in Table 6, as in the previous mode, some
joints passing from the LS limit in OCB frame is greater
than BRB, which shows a weakness of the system.
Table 6. Joints in an eight story frame under steady
lateral load pattern
Type Target
Displacement B IO LS CP C D E
OCB 12.38 0 4 0 3 0 7 0
BRB 13.25 0 12 0 2 0 0 0
Base Shear Curve-displacement under Lateral Load
Patterns in an Eight Story Frame
Figure 11. Base Shear Curve-displacement under Steady
Lateral Load
Figure 12. Base Shear Curve-displacement under Triangle
Lateral Load
Figure 13. Base Shear Curve-displacement under Lateral
Load of the First Mode
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Makara J. Technol. 1 April 2021 | Vol. 25 | No. 1
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The Description of Non-linear Dynamic Analysis of 8
Story Structure
Displacement and Relative Displacement of an Eight
Story Frame. Based on the seven mapping
accelerations applied to an eight story structure, the
displacement of story for OCB and BRB had a
decreasing trend. Additionally, the relative displacement
of the story in the buckling brace compared with
conventional braces had a special order and there were
few changes in each story toward the lower story.
Story Structure
Plastic Joints in a Ten Story Frame under Lateral
Loads. As shown in Table 8, some joints that pass from
the LS limit in the OCB frame are greater than the BRB,
which indicates the weakness of this type of system.
Table 7. Joints under Mapping Acceleration of the
Loma Prieta Earthquake in an 8 Story Frame
Type B IO LS CP C D E
OCB 1 10 0 4 0 8 0
BRB 0 17 3 0 0 0 0
Figure 14. The Maximum Displacement and Relative
Displacement of a Story under the Lome Prieta
Earthquake
Table 8. Joints in Five Story Frame under Lateral Load
Pattern of the First Mode
Type Target
Displacement B IO LS CP C D E
OCB 1762 0 9 3 1 0 8 2
BRB 17.38 0 13 2 0 0 0 0
Base Shear Curve-displacement under Lateral Load
Patterns in a Ten Story Frame
Figure 15. Base Shear Curve-displacement under a Steady
Lateral Load
Figure 16. Base Shear Curve-displacement under the
Triangular Lateral Load
Figure 17. Base Shear Curve-displacement under the
Lateral Load of the First Mode
Study of a Buckling Restrained Brace (BRB) in Steel Structures
Makara J. Technol. 1 April 2021 | Vol. 25 | No. 1
45
Description of Non-linear Dynamic Analysis of a Ten
Story Frame
Displacement and Relative Displacement of Ten
Story Frame. Based on seven mapping accelerations
applied to a ten story structure, the displacement of the
story for OCB and BRB had a decreasing trend. In the
relative displacement of stories in comparison with
conventional braces has a special order and there are
few changes in each story toward the lower story.
Table 9. Number of Joints under Mapping Acceleration
of Morgan Hil earthquake in a Ten Story
Frame
Type B IO LS CP C D E
OCB 1 6 0 0 0 12 0
BRB 0 11 2 0 0 0 0
Figure 18. The Maximum Displacement and Relative
Displacement of the Story under Morgan Hil
Earthquake
Story Structure
Plastic Joints in a 12 Story Frame under Lateral
Loads. As shown in Table 10, the number of joints that
passes from the LS limit in the OCB frame is greater
than BRB, which indicates the weakness of the system.
Table 10. Joints in 12 story frame under triangular
lateral load pattern
Type Target
Displacement B IO LS CP C D E
OCB 18.37 1 7 0 4 1 2 0
BRB 18.2 0 10 0 0 0 4 0
Base Shear Curve-displacement under Lateral Load
Patterns in 12 Story Frame
Figure 19. Base Shear Curve-displacement under the
Triangular Lateral Load
Figure 20. Base Shear Curve-displacement under Steady
Lateral Load
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Makara J. Technol. 1 April 2021 | Vol. 25 | No. 1
46
Figure 21. Base shear curve-displacement under the
Lateral Load of the First Mode
Table 11. Number of Joints Under Mapping Acceleration
of the Northridge Earthquake in a 12 Story
Frame
Type B IO LS CP C D E
OCB 0 21 0 4 0 8 0
BRB 1 11 1 0 0 5 0
Displacement and Relative Displacement of the 12
Story Frame
Figure 22. Displacement and Relative Displacement of the
Story under the Northridge Earthquake
Description of Non-linear Dynamic Analysis of a 12
Story Frame. Based on the number of joints under
mapping acceleration (Tables 7, 9 and 11), in the frames
with conventional braces, more joints pass from the LS
limit. Additionally, in the frames with BRB brace, the
number of made joints that did not pass from LS limit
was more toward the frames with OCB brace and the
trend of making plastic joints was based on the columns
with the braces with fewer stories. The use of a BRB
caused the transfer of force to the columns and
produced more joints in this area. In the frames with
OCB brace, the trend of making plastic joints was first
observed in the braces and then in the columns.
Based on the seven mapping accelerations applied to the
12 story structure, the displacement of stories for OCB
and BRB had a decreasing trend. The relative
displacement of stories compared with conventional
braces has a special order and there were few changes in
each story toward the lower story.
4. Conclusion
In this study, the strengthening of structures against
earthquakes were surveyed using buckling braces and
were analyzed using non-linear static and non-linear
dynamic analyses. Their function was investigated and
compared with conventional braces. The following
results were obtained: (a) Buckling braces with a
hysteresis curve had the same behavior in traction and
pressure, which caused an increase in plasticity and
more energy absorption of the structure. The BRB
presented and optimized behavior. (b) The BRB system
can be considered a desirable alternative for designing a
seismic load system because of the very high plasticity
and the suitable lateral hardness. (c) Buckling braces act
in most cases as a fuse and prevent the submission of
main members of the structure such as the columns.
(d) In all different types of lateral load, with increasing
elevation (or story), the base shear increase and the level
of performance of the structure decreases in the
structures modeled with 5, 8, 10 and 12 floors. (e) In
general, because of decreasing plastic joints in BRB
compared with the frames with the conventional brace,
the displacement of the story was less because of the
distribution of the relative displacement in the story.
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